Nonparametric statistics of dynamic networks with distinguishable nodes

2014/08/31 by Daniel Fraiman, Nicolas Fraiman, Ricardo Fraiman
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Artificial neural network #Complex Network Analysis Techniques #Component (thermodynamics) #Data space #Focus (optics) #Function (biology) #Graph theory and applications #Nonparametric statistics #Principal component analysis #Random Matrices and Applications #Statistical model #cond-mat.dis-nn #cond-mat.stat-mech #physics.data-an #q-bio.QM #stat.ME

paper · pdf · doi:10.1007/s11749-017-0524-8

24 pages, 6 figures. Title changed, Test (2017)

openalex publication_date 2017/01/28 · openalex created_date 2017/02/03 · arxiv created 2017/04/15 · arxiv updated 2017/04/18 · openalex updated_date 2026/08/06

Abstract

The study of random graphs and networks had an explosive development in the last couple of decades. Meanwhile, techniques for the statistical analysis of sequences of networks were less developed. In this paper we focus on networks sequences with a fixed number of labeled nodes and study some statistical problems in a nonparametric framework. We introduce natural notions of center and a depth function for networks that evolve in time. We develop several statistical techniques including testing, supervised and unsupervised classification, and some notions of principal component sets in the space of networks. Some examples and asymptotic results are given, as well as two real data examples.

Citations

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